What is expand (x^2-1)(dx-dy) ?

The solution to expand (x^2-1)(dx-dy) is x^2dx-x^2dy-dx+dy

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expand (x^2-1)(dx-dy)

expand

(x^{2} - 1) (d x - d y)

x^{2} d x - x^{2} d y - d x + d y

Solution steps

(x^{2} - 1) (d x - d y)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = x^{2}, b = - 1, c = d x, d = - d y

= x^{2} d x + x^{2} (- d y) + (- 1) d x + (- 1) (- d y)

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= x^{2} d x - x^{2} d y - 1 \cdot d x + 1 \cdot d y

Simplify

x^{2} d x - x^{2} d y - 1 \cdot d x + 1 \cdot d y : x^{2} d x - x^{2} d y - d x + d y

= x^{2} d x - x^{2} d y - d x + d y

(\frac{n + 2 x}{n})^{3}

- \frac{8 - 2 x ^{2} ( 4 - x ^{2} )}{3}

(\frac{1}{3} x + \frac{2}{3} y)^{2}

(\frac{2}{3} x^{6} + \frac{1}{4} y) (\frac{2}{3} x^{6} - \frac{1}{4} y)

3 l e f t (c - 6 b + 6 z)

What is expand (x^2-1)(dx-dy) ?
The solution to expand (x^2-1)(dx-dy) is x^2dx-x^2dy-dx+dy